Multivariate Multinomial Logit Model with ANOVA Decomposition for Correlated Outcomes

Music City Center 

Multivariate multinomial outcomes are often interdependent, yet most existing research on multinomial regression fits each outcome separately. This approach ignores correlations between outcomes, leading to loss of information and reduced predictive accuracy. Accounting for these correlations requires high-dimensional parameter spaces, making model estimation infeasible. This study proposes a multivariate multinomial logit model that captures outcome correlations and reduces parameter space dimension using ANOVA decomposition. The ANOVA decomposition enables explicit conditional model formulations, which allows a computationally much simpler composite likelihood approach. Then an efficient Minorization-Maximization (MM) algorithm that incorporates variable selection is developed. Simulation studies evaluate our method, demonstrating its effectiveness in parameter estimation and variable selection. The model is also applied to real-world data, revealing the correlation structure of multinomial choices. Our method outperforms existing approaches in predicting outcomes, offering significant advantages for predictive modeling and decision-making.

Multivariate analysis

Multinomial Logit

Composite Likelihood

ANOVA Decomposition

Correlated Outcomes

Variable Selection 

Biometrics Section